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**Areas**

Areas of some well-known figures are given below:

**Ex.1 A horizontal pipe for carrying floodwater has diameter 1 m. When water in it is 10 cm deep then the width of water surface AB is equal to ________ cm.**

**(1) 10 cm **

**(2) 25 cm (3) 60 cm **

**(4) 70 cm (5) None**

**Sol.**

Let O be the centre of circle.

In ΔOAD

502 = 402 + x2

2500 – 1600 = x^{2}

x^{2} = 900

x = 30

∴ AB = 2x = 60 cm. **Answer: (3)**

**Ex.2 Area of the shaded region is****(5) None of these**

**Sol.**

**Volume**

**Length of a diagonal:**

The length of diagonal of a cuboid =

The length of a diagonal of a cube =

**Ex.1 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4 circular rounds to reach the top of the building, then what will be total distance (in nearer metres) traveled by insect to reach the top? (1) 47 m **

**(2) 48 m **

**(3) 49 m **

**(4) 50 m**

**Sol. **Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance

of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the

pipe.

AO = πd = = 11m

BO = 5 m

AB = = = 12.08 m

Total distance traveled = 12.08 × 4 = 48.32 m

Hence distance in nearer meters = 48 m

**Ex.2 The surface area of a cube is 726 sq metres. Find the volume of the cube. (1) 1234 m ^{2} **

**(2) 1431 m ^{2}**

**(3) 1341 m **

**(4) 1331 m **

**(5) None of these**

**Sol. **Surface area S = 726 m** ^{2}** Volume V = ?

In a cube,

S = 6a

So, V = a

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